The mystery has been solved there is actually an answer to Hatters riddle.... evidently in 1896 by Lewis Carroll himself

The Riddle...Why is a raven like a writing desk?

The answer from Carroll's own pen... 'Because it can produce a few notes, though they are very flat; and it is nevar put with the wrong end in front!' (notice Carroll spelled never as "nevar" (raven...)

Carroll noted the following "Enquiries have been so often addressed to me, as to whether any answer to the Hatter's Riddle can be imagined, that I may as well put on record here what seems to me to be a fairly appropriate answer....This, however, is merely an afterthought; the riddle as originally invented, had no answer at all."